Spectral Envelope Representation using Sums of Gaussians

The aim of this paper is to present a new approach to spectral representation using sums of Gaussian distributions. Sums of Gaussians provide an intuitive representation for frequency bands of a signal spectrum as well as formant regions. The representation of spectral envelopes using Gaussian parameters {a, μ, σ} simplifies the expression of important tasks such as frequency warping and formant manipulation. Marquardt’s algorithm has been extended to estimate parameters of the Gaussian models for each frequency band, allowing each Gaussian parameter to be either optimized for fitting a given spectral sub-band, or else have a fixed value for reducing the number of model parameters. This allows for several choices on the sets of free/fixed parameters and the sizes of models. Experimental results show that the models proposed offer an accurate approximation of spectral envelope, and provide good perceptual results when applied to pitch shifting.